Mathematical Foundation of Computer Science

This textbook “Mathematical Foundation of Computer Science” has been designed to suit the needs of B. Tech. second year I semester and MCA first year students of JNTU, Hyderabad according to the revised syllabus. The students assigned with M. Tech., B. Sc., B.C.A. and IT related professional courses may also be benefited. Every topic has been started with necessary introduction and developed gradually up to the standard form. The theory part in each chapter has been given in a lucid explanation and number of examples has been worked out to illustrate the application of theory. Most of the worked out examples and unsolved problems in exercise have been taken from the previous examination paper of JNTU.

Chapter 1 Price: 2.99

Many proofs in Mathematics and many algorithms in Computer Science use logical expressions such as “If P then Q” or “If P1 and P2, then Q1 or Q2”. It is therefore, necessary to know the cases in which these expressions are either true or false. What we refer to as the truth values of such expressions. We discuss these issues in this unit.

Chapter 2 Price: 2.99

This chapter discusses various concepts such as the theory of inference in statement calculus, automatic theorem, the predicate logic, statement formulas in predicate logic, valid formulas and equivalences etc. It also has objective questions with solutions for all concepts discussed.

Chapter 3 Price: 2.99

The concept of a set underlies most of modern mathematics and much of Computer Science. To use sets as a foundation for all the other structures in this text, we first need to understand both the language used to describe sets and the operations normally associated with sets.

Chapter 4 Price: 2.99

In this unit we shall first explain what is meant by an algebraic system and then give several examples of familiar algebraic systems and discuss some of their properties. Here we will discuss about semigroups, monoids, groups and abelian groups.

Chapter 5 Price: 2.99

This unit explores concepts such as the basics of counting, combinations and permutations, binomial coefficients, combinatorial identities etc. It also has objective type questions with solutions for each of the concepts discussed.

Chapter 6 Price: 2.99

This unit elaborates on concepts such as generating functions of sequences, reccurence relations, solving reccurence relations by substitution generating functions, solution of inhomogeneous linear recurrence relations etc. It also consists of questions with solutions for all concepts discussed in the unit.

Chapter 7 Price: 2.99

Graph theory was born in 1736, with Euler’s paper on Konigsberg bridge problem. Euler, the father of graph theory, solved this long pending problem by means of a graph. The term graph is used frequently to denote the diagram of the real valued function y = f (x). But in graph theory we use the term graph as an object. Graphs are considered as discrete mathematical structures consisting of vertices and edges connecting the vertices.

Chapter 8 Price: 2.99

Graph theory begins with very simple geometric ideas which are used to conceptualize various complex systems in a much simpler way. It is applied in many areas such as Engineering, Computer Science, Economics, Sociology, Psychology, Linguistics etc. To a computer professional graph theory provides various techniques to study and analyze different problems associated with Computer design, Logic design, Operating systems, Formal languages, Artificial Intelligence, Code optimization. Information gathering and retrieval etc.,